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Re: Beginner Question

  • To: mathgroup at
  • Subject: [mg66587] Re: Beginner Question
  • From: "Scout" <Scout at>
  • Date: Sun, 21 May 2006 00:29:29 -0400 (EDT)
  • References: <e4mmb8$6iu$>
  • Sender: owner-wri-mathgroup at

"akil" <akil39 at>
news:e4mmb8$6iu$1 at
> Hi,
> Suppose I have three 2D points A, B, C.
> And two points, namely A and B form a line.
> How can I determine in mathematica on which side, (so which half-plane 
> formed by) of the line, point C is.
> So when I input three points I want to know if the third point is on the 
> left or right side of the half plane formed by the line (ray) A,B.
> Appreciate any help.

Well, the Dot Product can do better the work.
Below it's a simple procedure:

Let's start with a test function on a 2D point:

    In[1]:= point2DQ[x_] := VectorQ[x] && (Length[x] == 2);

Now, we can write the function that will decide on the A,B,C  points:

    In[2]:= whichPart[a_?point2DQ, b_?point2DQ, c_?point2DQ] :=
                    Module[{v1 = c - a, v2 = b - a},
                            (v1 . v2) / (Norm[v1]*Norm[v2])

If the whichPart[] function gives a negative number (< 0), then the C point 
is on the right if you move from A to B;
if it gives a positive number (> 0), then the C point is on the left if you 
move always from A to B;
and if it equals 1, then the 3 points are on the same line.


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